Place chocolate in bowl. In small saucepan, stir together sugar, rum and water over medium heat just until dissolved and bubbles appear at side. Pour over chocolate, whisking until smooth. Whisk in butter, in 2 additions.

Bake in centre of 350°F (180°C) oven until shiny and slightly puffed, about 22 minutes. Remove from pan; let cool for 10 minutes. (Make-ahead: Let cool completely; cover and refrigerate for up to 2 days. To unmould, dip each ramekin into pan of hot water for 20 seconds; turn out as directed.)

Run tip of small knife around side of each to loosen. Invert serving plate over dish. Turn over; lift off ramekin and remove paper. Spoon cherries on top. Serve warm or at room temperature.